Well, partially right. 1st gear is way lower on the 8 speed, and it does have a closer spread in the intermediate gears. The upper 3 gears are basically identical
1st gear on the 8 speed is 4.7 where as the 6 speed is only 3.23. So initial take off acceleration is way stronger on the 8 speed, plus add in the closer spacing of 2nd-5th gears. That is on paper and from my experience. When shopping for a truck in 2019, the first year for the 8 speed in the 2500's, I test drove several 2018 and older with the 6 speed and several 2019 with the 8 speed back to back. The 8 speeds definitely felt stronger but did wind up buying a super clean low mileage 2016 because it was $20k cheaper than a new 2019 at the time.
For highway cruising the top 3 gears are almost identical between the two trans, and those are the gears you will be in 99% of the time when cruising over 50 mph.
So yes, an 8 speed truck will feel much better on take off and stop and go driving with big tires. But cruising on the highway it will still feel a little sluggish with big tires.